Abstract
The main goal of this paper is to analyze the fan-mechanism of rotational motion transmission in a system of elastically bonded slabs on flat surface, simulating growth of shear ruptures in super brittle rocks. A physical model recently designed demonstrates that the fan-structure formation can be stable at the absence of distributed shear stress applied. The action of distributed shear stress causes the fan propagation as a wave representing the rupture head. The developed mathematical model of a fan-structure as a continuous system establishes the relation between the fan velocity and the fan length. It is shown that in the absence of friction the fan velocity may be arbitrary, but not greater than the limit velocity which is determined by the moment of inertia of slabs, the initial angle of their orientation and the elastic coefficient of bonds. In a system with friction the velocity of traveling fan is solely determined by the opening angle. The action of distributed shear stress leads to the instability start before the fan-structure completion. The fan length decreases with increasing velocity.
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Acknowledgements
This work was supported by the Centre for Offshore Foundation Systems (The University of Western Australia), the Complex Fundamental Research Program no. II.2P “Integration and Development”of SB RAS (project no. 0361-2015-0023) and the Russian Foundation for Basic Research (grant no. 14-01-00130).
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Tarasov, B.G., Sadovskii, V.M. (2017). Mathematical Modeling of Fan-Structure Shear Ruptures Generated in Hard Rocks. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science(), vol 10187. Springer, Cham. https://doi.org/10.1007/978-3-319-57099-0_74
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DOI: https://doi.org/10.1007/978-3-319-57099-0_74
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